CN111141602B - Method for synchronously determining drawing and pressing mold amount of asphalt mixture by utilizing indirect tensile test - Google Patents
Method for synchronously determining drawing and pressing mold amount of asphalt mixture by utilizing indirect tensile test Download PDFInfo
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Abstract
The embodiment of the invention discloses a method for synchronously determining the drawing and pressing mold quantity of an asphalt mixture by utilizing an indirect tensile test, which relates to the technical field of road engineering and adopts the technical scheme that the method comprises the following steps: s1: based on a double-modulus theory, obtaining a calculation formula of transverse and longitudinal deformation of the center of the indirect tensile test piece under different compression and tensile modulus ratios, wherein the calculation formula covers different test piece sizes and different center detection distances; s2: carrying out indirect tensile test on the asphalt mixture test piece, and actually measuring the transverse deformation and longitudinal deformation values at different central detection distances of two side surfaces of the test piece under the action of load by using a displacement meter; s3: and (3) setting corresponding solving targets, objective functions and constraint conditions by combining a calculation formula and the measured data and utilizing an Excel nonlinear programming program, and synchronously solving the drawing and pressing mold quantity and the drawing and pressing Poisson ratio of the test piece. The method is used for solving the problem that the pulling and pressing die quantities of the asphalt mixture cannot be synchronously analyzed in the prior art.
Description
Technical Field
The embodiment of the invention relates to the technical field of road engineering, in particular to a method for synchronously determining the drawing and pressing mold quantities of an asphalt mixture by utilizing an indirect tensile test.
Background
The asphalt mixture shows different modulus characteristics in a compression state and a tension state, and particularly, the compression modulus of the mixture is larger than the tension modulus. In order to accurately characterize the mechanical properties of the asphalt mixture, the tensile and compressive modulus characteristics of the asphalt mixture need to be quantitatively evaluated. The indirect tensile test is a mechanical test method commonly used in the field of road engineering, and in the method, a mixture test piece can be regarded as being in a two-dimensional tension-compression state, so that the compression modulus and the tension modulus of the test piece exist at the same time. However, in the modulus calculation method based on the indirect tensile test at the present stage, the test piece is regarded as only containing single modulus, which is not in accordance with the actual situation, and the tensile and compression modulus properties of the mixture can not be effectively analyzed.
The analysis of the tensile and compression molding quantity characteristics of the mixture needs the support of a double-modulus theory. In the aspect of double-modulus theoretical research, the soviet union amabartsumyan carries out a great deal of work and provides the following constitutive equation of the double-modulus material in a two-dimensional tensile and compressive stress state:
in the formula, epsilont、εcRespectively tensile strain and compressive strain, σt、σcRespectively tensile and compressive stress, Et、EcRespectively tensile modulus and compressive modulus, vt、vcRespectively, the larpoisson's ratio and the poisson's ratio. The constitutive equation can be coordinated and coexisted with a balance equation and a geometric equation in an elastic mechanics range, and is an effective tool for solving the problem of double modulus.
Therefore, if the results of the indirect tensile test are combined with the double-modulus theory of Ambartsumyan, the tensile and compression modulus characteristics of the mixture can be synchronously analyzed, but a corresponding method is not available at present.
Disclosure of Invention
Therefore, the embodiment of the invention provides a method for synchronously determining the pulling and pressing quantities of the asphalt mixture by using an indirect tensile test, so as to solve the problem that the pulling and pressing quantities of the asphalt mixture cannot be synchronously analyzed in the prior art.
In order to achieve the above object, the embodiments of the present invention provide the following technical solutions:
according to the embodiment of the invention, a method for synchronously determining the drawing and pressing mold quantity of an asphalt mixture by utilizing an indirect tensile test is provided, and the technical scheme is characterized by comprising the following steps:
s1: based on a double-modulus theory, obtaining a calculation formula of transverse and longitudinal deformation of the center of the indirect tensile test piece under different compression and tensile modulus ratios, wherein the calculation formula covers different test piece sizes and different center detection distances;
s2: carrying out indirect tensile test on the asphalt mixture test piece, and actually measuring the transverse deformation and longitudinal deformation values at different center detection distances of the first side surface and the second side surface of the test piece under the action of load by using a displacement meter;
s3: and (3) setting corresponding solving targets, objective functions and constraint conditions by combining a calculation formula and the measured data and utilizing an Excel nonlinear programming program, and synchronously solving the drawing and pressing mold quantity and the drawing and pressing Poisson ratio of the test piece.
Further, the S1 includes the following steps:
a1: based on the double-modulus constitutive equation formulas (1) - (3) in the background art and the actual stress distribution of the center of the indirect tensile test piece, the following calculation formula of the transverse and longitudinal deformation of the center of the test piece can be obtained through conversion,
in the formula, Lx、LyRespectively transverse and longitudinal deformation, P is the applied load amplitude, a is the width of the loading ram, t is the thickness of the test piece, EcIs the compressive modulus, n is the ratio of compressive modulus to tensile modulus, vcTo a Poisson's ratio, d1、d2、d3、d4Is the stress distribution coefficient related to the compression-tensile modulus ratio n;
a2: based on ABAQUS finite element software and a UMAT subprogram platform, calculating to obtain stress distribution coefficients corresponding to different compression-tension modulus ratios n, wherein the calculation formula of the stress distribution coefficients is d ═ a1n3+a2n2+a3n+a4Wherein a is1、a2、a3、a4To calculate the coefficients.
Further, the S2 includes the following steps:
b1: preparing an indirect tensile test piece and a loading pressure head.
Further, the test piece is cylindrical.
Further, the sizes of the test piece comprise diameters of 101.6 +/-0.25 mm and 150 +/-2.5 mm;
for a test piece with the diameter of 101.6 +/-0.25 mm, the central detection distance comprises three types, namely 25.4mm, 38.1mm and 50.8 mm;
for a test piece with a diameter of 150 + -2.5 mm, the center distances include four kinds of 25.4mm, 38.1mm, 50.8mm, and 76.2 mm.
Further, the S2 further includes the following steps:
b2: arranging displacement meters on the first side face and the second side face of the test piece to detect the deformation value of the center of the test piece under the load action, wherein the arrangement directions of the displacement meters comprise a transverse direction and a longitudinal direction, the longitudinal direction is a direction parallel to the load action, the transverse direction is a direction vertical to the load action, the center point of the test piece is taken as the midpoint of the displacement meter, the detection distance of the displacement meter at the center of the test piece can be determined according to any numerical value in the step B1, but the center detection distances corresponding to the two side faces of the test piece are different, and then, actually measuring to obtain 4 deformation data of different types, namely L1 x、L1 y、L2 x、L2 yWhere superscripts 1, 2 represent the two sides of the test piece and subscripts x, y represent the transverse and longitudinal directions.
Further, the S2 further includes the following steps:
b3: applying continuous hemiversine waveform load to the test piece, determining the load frequency and amplitude according to the test requirement, detecting the transverse and longitudinal deformation data of the centers of the first side surface and the second side surface of the test piece under the load action by using a displacement meter, and recording the applied load amplitude and the corresponding test piece deformation curve amplitude.
Further, the S3 includes the following steps:
c1: calling an Excel nonlinear programming program, and determining a solving target as a compression modulus EcA compression-tension modulus ratio n and a compression-poisson ratio vcThe objective function is that the error S between the calculated deformation and the measured deformation is minimum, wherein the calculation formula of the error S is shown as follows,
in the formula, L is a deformation value, superscripts 1 and 2 represent detection distances of different displacement meters corresponding to the first side surface and the second side surface of the test piece, subscripts x and y represent a transverse direction and a longitudinal direction, subscript cal represents a deformation value calculated according to the calculation formula in step S1, and subscript mea represents an actually measured deformation value obtained according to the test method in step S2;
c2: setting the constraint to 0 < EcN is more than or equal to 1 and V is more than 0c< 0.5, the initial value is set to Ec＝5000、n＝2、vcThe solver was set to a non-linear GRG at 0.3, and the resulting solution was used to obtain a compression modulus value EcAnd a compression-tensile modulus ratio n, further utilizing
The tensile modulus value E can be calculatedt。
The embodiment of the invention has the following advantages:
(1) the method for synchronously determining the tensile modulus and the compression modulus of the asphalt mixture by utilizing the indirect tensile test provided by the embodiment of the invention can synchronously measure two parameters of the tensile modulus and the compression modulus of the asphalt mixture based on one test, while the traditional method needs to respectively carry out direct tensile test and direct compression test to obtain the two parameters. Therefore, the method provided by the embodiment of the invention can greatly reduce the test workload.
(2) The method for synchronously determining the drawing and pressing mold amounts of the asphalt mixture by utilizing the indirect tensile test comprises the diameter of two common test pieces and the detection distance of several common sensors in the field of road engineering, and the method is high in applicability.
(3) The method for synchronously determining the drawing and pressing mold quantity of the asphalt mixture by utilizing the indirect tensile test provided by the embodiment of the invention is based on common office software of Excel in the solving process, is simple in operation process, is convenient for road engineering practitioners to use, and is strong in popularization.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It should be apparent that the drawings in the following description are merely exemplary, and that other embodiments can be derived from the drawings provided by those of ordinary skill in the art without inventive effort.
The structures, ratios, sizes, and the like shown in the present specification are only used for matching with the contents disclosed in the specification, so as to be understood and read by those skilled in the art, and are not used to limit the conditions that the present invention can be implemented, so that the present invention has no technical significance, and any structural modifications, changes in the ratio relationship, or adjustments of the sizes, without affecting the effects and the achievable by the present invention, should still fall within the range that the technical contents disclosed in the present invention can cover.
FIG. 1 is a general schematic diagram of a method for synchronously determining the amount of a drawing mold and a pressing mold of an asphalt mixture by using an indirect tensile test according to an embodiment of the invention;
FIG. 2 is a front view of a method for synchronously determining the amount of a drawing mold and a pressing mold of an asphalt mixture by using an indirect tensile test according to an embodiment of the present invention;
fig. 3 is a schematic mounting diagram of a displacement meter of the method for synchronously determining the pulling and pressing mold amounts of the asphalt mixture by using an indirect tensile test according to the embodiment of the invention.
In the figure: 1. a first side surface; 2. a second side surface; 3. a pressure head; 4. a displacement meter.
Detailed Description
The present invention is described in terms of particular embodiments, other advantages and features of the invention will become apparent to those skilled in the art from the following disclosure, and it is to be understood that the described embodiments are merely exemplary of the invention and that it is not intended to limit the invention to the particular embodiments disclosed. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the present specification, the terms "upper", "lower", "left", "right", "middle", and the like are used for clarity of description, and are not intended to limit the scope of the present invention, and changes or modifications in the relative relationship may be made without substantial changes in the technical content.
The method for synchronously determining the drawing and pressing mold amount of the asphalt mixture by using the indirect tensile test is shown in figures 1, 2 and 3 and comprises the following steps:
s1: based on a double-modulus theory, obtaining a calculation formula of transverse and longitudinal deformation of the center of the indirect tensile test piece under different compression and tensile modulus ratios, wherein the calculation formula covers different test piece sizes and different center detection distances;
s2: carrying out indirect tensile test on the asphalt mixture test piece, and actually measuring the transverse deformation and longitudinal deformation values of the first side surface 1 and the second side surface 2 of the test piece at different center detection distances under the action of load by using a displacement meter 4;
s3: and (3) setting corresponding solving targets, objective functions and constraint conditions by combining a calculation formula and the measured data and utilizing an Excel nonlinear programming program, and synchronously solving the drawing and pressing mold quantity and the drawing and pressing Poisson ratio of the test piece.
Wherein, S1 includes the following steps:
a1: based on the double-modulus constitutive equation formulas (1) - (3) in the background art and the actual stress distribution of the center of the indirect tensile test piece, the following calculation formula of the transverse and longitudinal deformation of the center of the test piece can be obtained through conversion,
in the formula, Lx、LyRespectively transverse and longitudinal deformation, P is the applied load amplitude, a is the width of the loading ram, t is the thickness of the test piece, EcIs the compressive modulus, n is the ratio of compressive modulus to tensile modulus, vcTo a Poisson's ratio, d1、d2、d3、d4Is the stress distribution coefficient related to the compression-tensile modulus ratio n.
A2: based on ABAQUS finite element software and UMAT subprogram platform, calculating to obtain stress distribution coefficients corresponding to different compression-tension modulus ratios n, and utilizingBy the formula d ═ a1n3+a2n2+a3n+a4Coefficient of distribution of counter stress d1、d2、d3And d4Fitting is performed, a1、a2、a3、a4Are fitting coefficients. The calculated stress distribution coefficient covers different test piece diameters and different center detection distances.
The test piece diameters include 101.6 +/-0.25 mm and 150 +/-2.5 mm. The center distances include three kinds of 25.4mm, 38.1mm, and 50.8mm for a test piece having a diameter of 101.6 + -0.25 mm, and four kinds of 25.4mm, 38.1mm, 50.8mm, and 76.2mm for a test piece having a diameter of 150 + -2.5 mm. The fitting results of the stress distribution coefficients corresponding to different specimen diameters and different center distances are summarized in table 1.
TABLE 1 summary of stress distribution coefficient fitting results
Wherein, S2 includes the following steps:
b1: an indirect tensile test piece and a loading ram 3 are prepared, and the test piece is cylindrical. The diameter of the test piece can be 101.6 +/-0.25 mm or 150 +/-2.5 mm, and the thickness of the test piece is not less than 20 mm. The inner diameter of the loading pressure head is consistent with the diameter of the test piece, and the width of the loading pressure head is 12.7mm for the test piece with the diameter of 101.6 +/-0.25 mm; for test pieces with a diameter of 150. + -. 2.5mm, the loading indenter width is 19.0 mm.
B2: the displacement meters 4 are arranged on two side faces of the test piece to detect the deformation value of the center of the test piece under the load action, the arrangement directions of the displacement meters 4 comprise transverse and longitudinal directions, the longitudinal direction is parallel to the load action, the transverse direction is perpendicular to the load action, the displacement meters 4 use the center point of the test piece as the midpoint, and the detection distance is determined according to the center detection distance given in the table 1. For the same side, the lateral displacement meter and the longitudinalThe detection distances to the displacement meters are set to be the same, but the center detection distances corresponding to the first side surface 1 and the second side surface 2 of the test piece are different, so that the displacement meter 4 can detect deformation values of 4 different types, namely L1 x、L1 y、L2 x、L2 yWherein, superscripts 1, 2 represent the detection distances of different displacement meters 4 corresponding to the first side 1 and the second side 2 of the test piece, and subscripts x, y represent the transverse direction and the longitudinal direction.
B3: applying continuous hemiversine waveform load to the test piece, wherein the load frequency and the load amplitude can be determined according to the test requirement, detecting the transverse and longitudinal deformation data of the centers of the first side surface 1 and the second side surface 2 of the test piece under the load action by using the displacement meter 4, and recording the applied load amplitude and the corresponding test piece deformation curve amplitude.
S3 includes the steps of:
c1: calling an Excel nonlinear programming program, and determining a solving target as a compression modulus EcA compression-tension modulus ratio n and a compression-poisson ratio vcThe objective function is that the error S between the calculated deformation and the measured deformation is minimum, wherein the calculation formula of the error S is shown as follows,
in the formula, L is a deformation value, the superscripts 1 and 2 represent detection distances of different displacement meters 4 corresponding to the first side surface 1 and the second side surface 2 of the test piece, the subscripts x and y represent the transverse direction and the longitudinal direction, the subscript cal represents a deformation value calculated according to the calculation formula in the step S1, and the subscript mea represents an actually measured deformation value obtained according to the test method in the step S2;
c2: setting the constraint to 0 < EcN is more than or equal to 1 and V is more than 0c< 0.5, the initial value is set to Ec＝5000、n＝2、vcThe solver was set to a non-linear GRG at 0.3, and the resulting solution was used to obtain a compression modulus value EcAnd a compression-tensile modulus ratio n, further utilizing
The tensile modulus value E can be calculatedt。
In this example, the asphalt mixture was subjected to an indirect tensile test, taking a specimen having a diameter of 101.6mm and a thickness of 40mm as an example.
The lateral and longitudinal displacement meters are fixed to both sides of the test piece, and referring to table 1, the detection interval of the lateral and longitudinal displacement meters 4 of the first side surface 1 of the test piece is set to 25.4mm, and the detection interval of the lateral and longitudinal displacement meters 4 of the second side surface 2 is set to 50.8 mm.
And applying continuous hemiversine waveform load to the test piece, wherein the load amplitude is 1000N. The transverse displacement amplitude value corresponding to the first side surface 1 of the test piece under the action of the load is L through the detection of the displacement meter 41 x-mea3.61 μm with a longitudinal displacement amplitude L1 y-meaThe transverse displacement amplitude corresponding to the second side 2 of the test piece is L, 5.35 μm2 x-mea5.82 μm with a longitudinal displacement amplitude L2 y-mea＝11.63μm。
Synchronously solving the drawing and pressing mold quantity of the test piece by using an Excel nonlinear programming program, and determining a solving target as a pressing modulus EcA compression-tension modulus ratio n and a compression-poisson ratio vcThe constraint condition is set to 0 < EcN is more than or equal to 1 and V is more than 0c< 0.5, the initial value is set to Ec＝5000、n＝2、vcThe solver was set to a non-linear GRG with the objective function being the minimum error S between the calculated and measured deformations, S being calculated using equation (6).
Wherein, the calculated values L of the transverse and longitudinal deformation of the first side surface 1 and the second side surface 2 of the test piece in the formula (6)1 x-cal、L1 y-cal、L2 x-calAnd L2 y-calThe calculation was performed by using equations (4) and (5). Stress coefficients d corresponding to the equations (4) and (5)1、d2、d3、d4Using the formula d ═ a1n3+a2n2+a3n+a4Performing calculation to calculate coefficient a1、a2、a3And a4Table 1 may be consulted. Inquiring according to the size of the test piece and the detection distance of the displacement meter 4Fitting coefficient a of the obtained stress coefficient1、a2、a3And a4As shown in table 2.
TABLE 2 fitting coefficients of stress coefficients corresponding to the test pieces
The information is integrated, an Excel nonlinear programming program is used for solving, and the solving result is Ec＝2495MPa、n＝2.54、vc＝0.11，
The tensile modulus of the test piece is further calculated as
The Poisson's ratio is further calculated as
In summary, the press modulus and the draw modulus of the test piece were 2495MPa and 982MPa, respectively, and the press Poisson ratio and the Laisson ratio were 0.11 and 0.04, respectively.
Although the invention has been described in detail above with reference to a general description and specific examples, it will be apparent to one skilled in the art that modifications or improvements may be made thereto based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (3)
1. The method for synchronously determining the drawing and pressing mold amount of the asphalt mixture by utilizing the indirect tensile test is characterized by comprising the following steps of: the method comprises the following steps:
s1: based on a double-modulus theory, obtaining a calculation formula of transverse and longitudinal deformation of the center of the indirect tensile test piece under different compression and tensile modulus ratios, wherein the calculation formula covers different test piece sizes and different center detection distances;
the S1 includes the steps of:
a1: based on dual-modulus constitutive equation formulas (1) - (3):
and the actual stress distribution of the center of the indirect tensile test piece can be converted to obtain the following calculation formula of the transverse and longitudinal deformation of the center of the test piece,
in the formula, Lx、LyRespectively transverse and longitudinal deformation, P is the applied load amplitude, a is the width of the loading pressure head, t is the thickness of the test piece, n is the ratio of the compression modulus to the tensile modulus, d1、d2、d3、d4Is a stress distribution coefficient, ε, depending on the compression-tensile modulus ratio nt、εcRespectively tensile strain and compressive strain, σt、σcRespectively tensile and compressive stress, Et、EcRespectively tensile modulus and compressive modulus, vt、vcRespectively, the larpoisson ratio and the poisson pressure ratio;
a2: based on ABAQUS finite element software and a UMAT subprogram platform, calculating to obtain stress distribution coefficients corresponding to different compression-tension modulus ratios n, wherein the calculation formula of the stress distribution coefficients is d ═ a1n3+a2n2+a3n+a4Wherein a is1、a2、a3、a4To calculate the coefficients;
s2: carrying out indirect tensile test on the asphalt mixture test piece, and actually measuring the transverse deformation and longitudinal deformation values of different centers of the first side surface (1) and the second side surface (2) of the test piece at different distances under the action of load by using a displacement meter (4);
the S2 includes the steps of:
b1: preparing an indirect tensile test piece and a loading pressure head (3), wherein the test piece is cylindrical, and the size of the test piece comprises two types of diameters of 101.6 +/-0.25 mm and 150 +/-2.5 mm;
for a test piece with the diameter of 101.6 +/-0.25 mm, the central detection distance comprises three types, namely 25.4mm, 38.1mm and 50.8 mm;
for a test piece with the diameter of 150 +/-2.5 mm, the central detection distance comprises four types of 25.4mm, 38.1mm, 50.8mm and 76.2 mm;
b2: arranging displacement meters (4) on the first side surface (1) and the second side surface (2) of the test piece to detect the deformation value of the center of the test piece under the load action, wherein the arrangement directions of the displacement meters (4) comprise a transverse direction and a longitudinal direction, the longitudinal direction is parallel to the load action, the transverse direction is perpendicular to the load action, the center point of the test piece is taken as the midpoint of the displacement meters (4), the detection distance of the displacement meters (4) at the center of the test piece can be determined according to any value in the step B1, but the center detection distances corresponding to the first side surface (1) and the second side surface (2) of the test piece are different, and then, actually measuring to obtain deformation data of 4 different types, namely L1 x、L1 y、L2 x、L2 yWherein the superscripts 1, 2 represent the first side (1) and the second side (2) of the test piece, and the subscripts x, y represent the transverse direction and the longitudinal direction;
s3: and (3) setting corresponding solving targets, objective functions and constraint conditions by combining a calculation formula and the measured data and utilizing an Excel nonlinear programming program, and synchronously solving the drawing and pressing mold quantity and the drawing and pressing Poisson ratio of the test piece.
2. The method for synchronously determining the drawing and pressing mold quantity of the asphalt mixture by using the indirect tensile test according to claim 1, is characterized in that: the S2 further includes the steps of:
b3: applying continuous hemiversine waveform load to the test piece, determining the load frequency and amplitude according to the test requirement, detecting the transverse and longitudinal deformation data of the centers of the first side surface (1) and the second side surface (2) of the test piece under the load action by using a displacement meter (4), and recording the applied load amplitude and the corresponding test piece deformation curve amplitude.
3. The method for synchronously determining the drawing and pressing mold quantity of the asphalt mixture by using the indirect tensile test according to claim 1, is characterized in that: the S3 includes the steps of:
c1: calling an Excel nonlinear programming program, and determining a solving target as a compression modulus EcA compression-tension modulus ratio n and a compression-poisson ratio vcThe objective function is that the error S between the calculated deformation and the measured deformation is minimum, wherein the calculation formula of the error S is shown as follows,
in the formula, L is a deformation value, superscripts 1 and 2 represent detection distances of different displacement meters corresponding to two side surfaces of the test piece, subscripts x and y represent a transverse direction and a longitudinal direction, subscript cal represents a deformation value calculated according to a calculation formula in step S1, and subscript mea represents an actually measured deformation value obtained according to the test method in step S2;
c2: setting the constraint to 0 < EcN is more than or equal to 1 and V is more than 0c< 0.5, the initial value is set to Ec＝5000、n＝2、vcThe solver was set to a non-linear GRG at 0.3, and the resulting solution was used to obtain a compression modulus value EcAnd a compression-tensile modulus ratio n, further utilizing
The tensile modulus value E can be calculatedt。
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